Problema de Yamabe modificado em variedades compactas de dimensão quatro e métricas críticas do funcional curvatura escalar

• Autor(a) principal: Santos, Alex Sandro Lopes
• Data de Publicação: 2017
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Repositório Institucional da Universidade Federal do Ceará (UFC)
• Texto Completo: http://www.repositorio.ufc.br/handle/riufc/22885
• topic: Problema de Yamabe; Curvatura biortogonal; Variedade compacta; Curvatura escalar; Métricas críticas; Variedade Einstein; Yamabe problem; Biorthogonal curvature; Compact manifolds; Scalar curvature; Critical metrics; Einstein manifolds

In the fisrt part of this work we investigate the modified Yamabe problem on four-dimensional manifolds whose the modifiers invariants depending on the eigenvalues of the Weyl curvature tensor and they are described in terms of maximum and minimum of the biorthogonal (sectional) curvature. We provide some geometrical and topological properties on four-dimensional manifolds in terms of these invariants. In the second part we investigate the critical points of the total scalar curvature functional restricted to space of metrics with constant scalar curvature of unitary volume, for simplicity CPE metrics. It was conjectured in the 1980’s that every CPE metric must be Einstein. We prove that such a conjecture is true under a second-order vanishing condition on the Weyl tensor.